The vast amounts of data coming, for example, from a number of sensors create data transmission and processing problems that are largely caused by the sheer bulk of the incoming information. As a consequence, a number of techniques have evolved for reducing or otherwise compressing the incoming data without compromising the information content. The design of a data compressor for nearly any type of data must address three important considerations. First, the degree that the data is statistically redundant must be determined; second, the true information content of the data by a particular user must be established and; third, the tolerable degree of distortion of the data for a particular user must be defined. Usually, satisfying the first consideration takes care of the third to fix the amount of compression with tolerable distortion. If this amount of compression is not sufficient, then other schemes must be considered that might distort the original data. In this case the second and third considerations determine the type and extent of data compression chosen at the expense of some distortion.
Contemporary data compressors have generally been designed for cases where the data is highly redundant and all of the original signal is assumed to be of interest to the user. Acoustic surveillance data, however, is not highly redundant within the frequency bandwidth of interest; thus, the prospects for distortionless compression are rather meager. Furthermore, only a small fraction of the total signal power is usually of interest to a user, that is, that portion which represents the narrowband "line" components in the signal. The broadband power which constitutes most of the signal is useless insofar as signal processing is concerned. Hence, a noisy-source encoding approach is required for an effective solution to the acoustic data compression problem.
The problem of optimum source encoding for a signal corrupted by noise has been addressed in the literature for the case of a frequency-weighted mean-squared error (WMSE) distortion measure. A thorough analysis of this problem is defined by R. L. Dobrushin and B. S. Tsybakov in their article entitled "Information transmission with additional noise," IRE Trans. Inform. Theory, vol. IT-8, pp. 293-304, September 1962; J. K. Wolf and J. Ziv in their article entitled "Transmission of noisy information to a noisy receiver with minimum distortion," IEEE Trans. Inform. Theory, Vol. IT-16, pp. 406-411, July 1970; and T. Berger, Rate Distortion Theory, Englewood Cliffs, N.J.: Prentice-Hall, 1971.
By way of example, the problem can be better visualized by noting FIG. 1 and its typical optimum communication system 10. Although the WMSE distortion measure tends to be a rather poor choice for acoustic signals, the system shown will serve as a starting point. A source 11 of signals s includes an analog family of narrowband components which are received in a background of additive broadband noise n represented by source 12. An optimum encoder 13 first computes the minimum mean-squared error estimate of s given x in a conditional mean computer 14. This estimate, u, is simply the conditional mean E.sub.x (s) of s given x, and is implemented in the case of Gaussian signal and noise by an infinite-lag Wiener filter, see A. Papoulis, Probability Random Variables, and Stochiastic Processes, New York: McGraw-Hill, 1965.
The final step is to encode u in encoder 15 for minimum-rate transmission over the communications link with respect to the WMSE distortion measure. Again in the Gaussian case, this can be achieved by performing a Karhunen-Loeve transform on the quantized coefficients a.sub.k. Transmission over a data link 16 to a decoder section 17 delivers decoded data from a decoder 18 to the user in the form s=E.sub.y u.
In practice, the optimum communication system referred to above only can be approximated due to the constraints of finite processing times and unknown nonstationary signal statistics. If we assume Gaussian signals and noise, the computation of u can be implemented by an adaptive, finite-length Wiener filter. Furthermore, the Karhunen-Loeve transformation in the encoder (an exceedingly difficult computation) may be replaced by the more facile Fourier transform. These two transforms are asymptotically equivalent as the integration time approaches infinity. For a further analysis of this technique please see J. Pearl, "On coding and filtering stationary signals by discrete Fourier transforms," IEEE Trans, Inform. Theory, vol. IT-19, pp. 229,232, March 1973. Finally, the weighted-variance quantization may be accomplished by estimating the coefficient variance and using a predetermined weighting rule. This along with the other considerations enumerated above are balanced against one another to arrive at an acceptable compromise. The state-of-the-art has failed to provide an acceptable compromise particularly adaptable to the highly noisy information coming from a number of acoustic monitors receiving narrowband "line" information amongst ever present Gaussian white noise.